Estimating a time-dependent concordance index for survival prediction models with covariate dependent censoring

Given a predictive marker and a time-to-event response variable, the proportion of concordant pairs in a data set is called concordance index. A specifically useful marker is the risk predicted by a survival regression model. This article extends the existing methodology for applications where the length of the follow-up period depends on the predictor variables. A class of inverse probability of censoring weighted estimators is discussed in which the estimates rely on a working model for the conditional censoring distribution. The estimators are consistent for a truncated concordance index if the working model is correctly specified and if the probability of being uncensored at the truncation time is positive. In this framework, all kinds of prediction models can be assessed, and time trends in the discrimination ability of a model can be captured by varying the truncation time point. For illustration, we re-analyze a study on risk prediction for prostate cancer patients. The effects of misspecification of the censoring model are studied in simulated data.